Truth and Logic – Or how Logic is a useful mental tool, but not a path for a mind of light

"Logic can only tell us what's valid and what's invalid, based on what we've presumed to be valid. It cannot tell us what's true since Truth is a trans-rational concept." - some guy on an alternative SM

That’s quite a mouthful and something that seems contradictory to what we’ve been taught. Without stating that logic is bad or useless, it sets its scope and defines a meaningful relationship to Truth, which is described as a trans-rational concept. In other words, Truth is an idea (Plato would call this an archetype, one of the fundamental ones at that), going beyond what logic works with.

Truth and Logic in Data Science Terms

In my line of work where everything sooner or later boils down to variables, I like to think of this as follows: Truth is a continuous variable and logic is the process of generating and utilizing binary variables, to model. However, all predictive models are but approximations of what we are trying to predict, in this case, the continuous variable. Some would say that perfect predictions aren't possible or meaningful, but this is just a proxy, a model of sorts, for me to understand this idea better. So let's not over-analyze it!

Logic is powerful and without it, we don't have a chance of doing anything in this world, as a species that likes to call itself rational. If we were to give up our rationality (like some people have lately), regressing to the animal state or ascending to a divine one, we'd be a different kind of being. But let's not get too metaphysical now and stay on the physical stuff. Logic is something Aristotle and several other philosophers (e.g., Descartes) valued greatly. Nowadays it has elevated itself into a science of sorts and some people do Logic for a living (i.e., logicians), mostly in academia. After all, Logic is quite theoretical at its core, even if most of its applications are very hands-on. You could argue that the whole field of Computer Science wouldn't have been possible if it weren't for individuals like Ada Lovelace and Alan Turing who managed to bridge the two worlds: that of Math and that of Applied Math. The latter evolved, through the leveraging of Logic, to become the Science of Computing, even if the foundations for this were laid long before either one of these individuals.

Logic works with discrete data, primarily binary variables. Through its various operators, it can describe and process logical relationships and even make some basic inferences. Statistics professionals love all this, though it's doubtful that most of them understand it the same way that logicians and scientists do. After all, Science itself can be viewed as an application of Logic, while it's hard to do anything meaningful in science without using Logic quite a bit, even if it's on the more abstract level (reasoning). Modern scientific fields, such as Artificial Intelligence, make use of Logic too, though in different ways than Statistics does. After all, A.I. is a scientific field, while Statistics is a sub-field at best, and the way it is used, it’s hardly scientific.

Perhaps all this is why Logic is useful, but not sufficient in describing Truth. The latter is more akin to a fractal of sorts, an object of infinite length or area, dwelling in a dimension that's between two numbers (so most fractals you see drawn on a plane are of dimensionality n, where n is a number between 2 and 3). Truth is more complex than most common fractals though since it spans beyond our 3-D world. Perhaps that's why it's hard to agree on something 100% since the Truth of it is in that in-between space, which is next to impossible for the rational mind to grasp. Maybe that's why it's a trans-rational concept, an idea that requires more than Logic to comprehend and perhaps even to express.

Truth and the “Mind of Light”

If we were to know the Truth (as most philosophers and scientists have attempted, with varied results), we’d experience what I call a “mind of light” whereby things seem connected and part of a whole, while those that are not connected are jettisoned (a more attainable form of enlightenment). This connectivity of knowledge is often modeled through graphs and some specialized data modelers do just that (aka ontologists, not to be confused with the oncologists who study cancer). Ontologists model data using networks/graphs and provide insights and ideas as to how to optimize information flows and data structures, accordingly. Of course, ontologists don't necessarily have a mind of light, but they certainly perceive the world of data more holistically than most data professionals, including most data scientists. There is something transcendental about graphs/networks that only a few people truly understand.

Euler as an Example of a Truth-bound Individual

One such person is Euler who was probably the best mathematician after Pythagoras. Interestingly, he could tackle any problem he got his hands on, from abstract math (e.g., number theory) to applied math to even engineering. Perhaps he was aware of Truth more than most people of his time (or even our time).

Still, Euler wasn’t a logician or even remotely infatuated with Logic. He used it, for sure, but he never really paid much attention to logical gates and such, since, like most Math professionals, he was more concerned with Mathematics, rather than the engine of his craft. Similarly today, most data scientists are concerned with insights and data products, rather than the inner workings of their models. Let data engineers deal with the latter! Perhaps that’s why there is so little real innovation in data science nowadays as it tends to borrow more and more from A.I. and other fields.

Final Words

I could write more about this topic but it wouldn’t be long before it starts to appeal like rumbling. Traversing through various seemingly disconnected ideas often does. Most of the articles I write on my blog tend to be shorter and more focused (you could say, more Logic-driven), though with the same commitment to Truth. After all, isn't that what science is all about? Feel free to let me know of your (truthful) thoughts and insights in the comments below. Cheers!